Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate

Abstract

In this paper, we study the dynamics of an infectious disease in the presence of a continuous-imperfect vaccine and latent period. We consider a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population. After we propose the model, we provide the well-posedness property and calculate the effective reproduction number . Then, we obtain the threshold dynamics of the system with respect to by studying the global stability of the disease-free equilibrium when and the system persistence when . For the endemic equilibrium, we use the semi-discretization method to analyze its linear stability. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to implement a case study regarding data of influenza patients, study the local and global sensitivity of , construct approximate stability charts for the endemic equilibrium over different parameter spaces and explore the sensitivity of the proposed model solutions.

Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system

“…Examples include the time-delayed feedback in laser systems [ 46 ] and control of chaos in Belousov–Zhabotinsky reactions [ 37 ]. DDEs also have a broad range of applications in biological systems [ 58 ], including epidemic spreading such as the ongoing COVID-19 pandemic [ 4 , 45 ], propagation of action potentials between neurons [ 9 , 51 ], tumor growth [ 71 ], population dynamics [ 42 , 70 ] and respiratory model [ 22 ]. Other DDE applications in engineering and technology include electrical transmission lines [ 10 ], electrodynamics of interacting charged particles [ 27 ], machine tool vibrations [ 34 ], control of robotic machines [ 40 , 43 , 49 ] and model of shimming wheels [ 67 ].…”

Vaccination control of an epidemic model with time delay and its application to COVID-19

“…Consider the SEIR-type epidemic model with time delay and vaccination control which is presented as following functional differential equation: where all parameters are nonnegative (see Table 1 for details), u ( t ) is a vaccination control needed to design. u ( t ) can be seen as a vaccination rate [ 13 , 28 ]. The flow diagram for model ( 1 ) is presented in Fig.…”

Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

“…Furthermore, is the corresponding value of the th iteration of the discretization equation. From AI-Darabsah [13] , Zhao and Jiang [37] , Liu et al. [38] , Zhang and Jiang [39] , Arino et al.…”

“…According to a 2005 WHO report, the eradication of smallpox has been considered the most spectacular success of routine vaccination. Thus, some basic epidemic models with vaccination strategies have been studied in the last several decades [9] , [10] , [11] , [12] , [13] . In [9] , Liu et al.…”